Turns out, the turkey day love birds were hosted by Gwyneth Paltrow at a dinner party at her London home.

"Gwyneth seems to have played a role in their relationship," the source told Us, intimating that the Oscar winning actress set up the new "it" couple in Hollywood.

Paparazzi have been hot on their heels, and it's caused some problems -- according to X17online.com on Friday, Gyllenhaal and Swift, being tailed in Jake's car by photographers, called the Los Angeles Police Department, who sent in ground support and even an helicopter escort.